Okay, I'll admit up front that I have no specialized knowledge (other than first hand experience) about this thing called "string of pearls" disease... but I do have some time to kill so let me ruminate and ramble on this topic. First of all, this whole condition in ill-defined... "string-of-pearls" is obviously just a reference to a single symptom and not even a complete description of a condition let alone naming a disease. There is no clue as to cause and effect.... at least the alternate terminology "protein poisoning" leads one to certain assumptions about the likely causes. I've seen mention elsewhere on the Internet trying to link the outward appearance of the dying worm to being bloated (gas) in obvious reference to the "pearls" however to my eye it looks like the "string" is the deformed part of the worm and it would suggest perhaps parts of the worm is being dissolved. And then there's these occasional references to cold... I'm not sure how temperature plays into this but the one time I experience worms with the condition it was pretty warm (60-70F) in the basement. Right now my worm bins are out in the unheated garage in the dead of winter and I'm measuring bedding temperatures below 40F and no problems... they also have literally mountains of food to munch on (and surprisingly are working on those piles, albeit slowly). As a sideline: I have two bins of Africans, which are reputed to die at anything under 50F... they too are out in the cold garage and though these guys are not eating hardly compared to the Euros and Red Wigglers, they are nevertheless alive and appear in good shape and leave me no doubt they will survive this winter without issue. My conclusion is that cold has no bearing on the condition called "string-of-pearls". Some things I know from other activities/hobbies I've been involved with in the past: too much simple sugars will often lead to fermentation build-up of alcohols and phenols, while excess protein can degrade to build-up ammonia concentrations. Also there are food stuff which contain proteolytic enzymes, such as papain (in papaya) and bromelain (in pineapple) that will slowly dissolve protein molecules... worms are almost entirely made up of protein... think about it. I will go back to my original observation that the weird part is the "strings" and not the "pearls". Based upon this my thinking is that something is dissolving the worms rather than the worms are blowing-up. Thus I might suggest that worms always be fed in one section of the bin and not scattered all over the surface... also I would suggest large amounts of high-protein be limited or mixed with more "carbs" and finally I'd try to keep the concentration of simple sugars to quantities that fermentation yeast/bacteria can process at a rate the worms can consume without flooding their bedding. As a wrap up to my ramblings here: Do I know what this "string-of-pearls" disease is? No... but I don't believe anyone else on the Internet knows for sure either. Thus everyone is entitled to their guesses. And now you have mine.

Yes, agree with LilBit, definitely means more water. I find that they need more water than most succulents. Mine is just some small cuttings from a store, and since they aren't in gritty mix either, I thought I would water them less and they soon became wrinkled and ill-looking for quite awhile....until I decided to water them few days in a roll and it was like filling water balloons with water. Now I water them whenever the top inch of the soil is dry. Before After

Just cut all the healthy parts off. Put new soil in the pot. It would really be beneficial if you got pumice or perlite. Mix half pumice or perlite and half C&S mix in your pot. Just lay the healthy strands on the soil and they should root for you in a couple of wks. Do not water until roots form. This plant is easy to bring back to life. They also root pretty quickly:).

I believe your problem is a soil issue along with not enough light. These are easy to fix. I put a video below from Desert Plants of Avalon. I like her videos:). There are two things I don't agree with from the video, she mists the cuttings right after she plants them up. I like to wait to water till I see roots. The other thing I disagree with her on is she uses sand in her mix. I find sand can be problematic. I would get some perlite or pumice. Whatever is easier to get. Do a mix of 50% perlite or pumice with 50% C&S soil. Once you get roots I would suggest a place where there is brighter light. With these if you put them in the direct sun they turn a tan color, and lose that pretty green color. At least in my experience. One last thing make sure there are drainage holes. You have such a nice plant hopefully you can save it. Goodluck:).